Abstract : The Fisher vector (FV) representation is a high-dimensional extension of the popular bag-of-word representation. Transformation of the FV by power and L2 normalizations has been shown to significantly improve its performance. With these normalizations included, this representation has yielded state-of-the-art results for a wide number of image and video classification and retrieval tasks. The normalizations, however, render the representation non-additive over local descriptors. Combined with its high dimensionality, this makes the FV computationally very expensive for the purpose of localization tasks. In this paper we, first, present approximations to both these normalizations, which yield significant improvements in the memory requirements and computational costs of the FV when used for localization. Second, we show how these approximations can be used to define upper-bounds on the score function that can be efficiently evaluated, which paves the way for the use of branch-and-bound search as an alternative to exhaustive scanning window search. We present experimental evaluation results on classification and temporal localization of actions in videos. These show that the proposed approximations lead to speed-ups of at least one order of magnitude, while maintaining state-of-the-art action localization performance.